Question

Find the amount and the compound interest on ₹ 10,000 for two years at 5% per annum

compounded yearly​

Answer 1

Answer:

interest on Rs 10,000 for 1

2

1

years at 10% per annum, compounded half yearly. Would this interest be more than the interest he would get if it was compounded annually?

Answer 2

${\large{\boxed{\underline{\mathrm{\bf{\orange{Given:-}}}}}}}$

• Sum of money (Principal) = ₹10,000
• Rate of Interest = 5% p.a.
• Time = 2 years

${\large{\boxed{\underline{\mathrm{\bf{\red{To \ Find:-}}}}}}}$

• Amount and Compound Interest

${\large{\boxed{\underline{\mathrm{\bf{\pink{Formula \ Used:-}}}}}}}$

$\bigstar \ {\boxed{\tt{\green{C.I. = P \ \bigg [ \bigg ( 1 + \dfrac{R}{100} \bigg ) ^n - 1 \bigg ] }}}} \ \bigstar$

where,

• C.I. = Compound Interest
• P = Principal i.e. ₹10,000
• R = Rate of Interest i.e. 5% p.a.
• n = Time period i.e. 2 years

$\bigstar \ {\boxed{\tt{\red{A = P + I}}}} \ \bigstar$

where,

• A = Amount
• P = Principal
• I = Interest

${\large{\boxed{\underline{\mathrm{\bf{\blue{Solution:-}}}}}}}$

Let, the time be n.

Given :-

• Sum of money (Principal) = ₹10,000
• Rate of Interest = 5% p.a.
• Time = 2 years

According to the question by using the formula of Compound Interest, we get,

$\longmapsto {\mathsf{C.I. = Rs. \ 10,000 \ \bigg [ \bigg ( 1 + \dfrac{5}{100} \bigg ) ^2 - 1 \bigg ] }}$

$\longmapsto {\mathsf{C.I. = Rs. \ 10,000 \ \bigg [ \bigg ( \dfrac{100 + 5}{100} \bigg ) ^2 - 1 \bigg ] }}$

$\longmapsto {\mathsf{C.I. = Rs. \ 10,000 \ \bigg [ \bigg ( \dfrac{105}{100} \bigg ) ^2 - 1 \bigg ] }}$

$\longmapsto {\mathsf{C.I. = Rs. \ 10,000 \ \bigg [ \bigg ( \dfrac{21}{20} \times \dfrac{21}{20} \bigg ) - 1 \bigg ] }}$

$\longmapsto {\mathsf{C.I. = Rs. \ 10,000 \ \bigg [ \dfrac{441}{400} - 1 \bigg ] }}$

$\longmapsto {\mathsf{C.I. = Rs. \ 10,000 \ \bigg [ \dfrac{441 - 400}{400} \bigg ] }}$

$\longmapsto {\mathsf{C.I. = Rs. \ 10,000 \ \times \dfrac{41}{400}}}$

$\longmapsto {\mathsf{C.I. = Rs. \ \dfrac{4,10,000}{400}}}$

$\Longrightarrow {\mathsf{C.I. = Rs. \ 1025}}$

${\orange{\bigstar}} \ \therefore {\boxed{\underline{\mathsf{\green{Compound \ Interest}{\red{ \ is \ }{\blue{\bf{Rs. \ 1025}}}}}}}} \ {\orange{\bigstar}}$

According to the question by using the formula of Amount, we get,

$: \longmapsto {\mathsf{Amount = Rs. \ (10,000 + 1025)}}$

$: \longmapsto {\mathsf{Amount = Rs. \ 11,025}}$

${\orange{\bigstar}} \ \therefore {\boxed{\underline{\mathsf{\green{Amount}{\red{ \ is \ }{\blue{\bf{Rs. \ 11,025}}}}}}}} \ {\orange{\bigstar}}$